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ZOJ Problem Set - 3575
Under Attack III

Time Limit: 7 Seconds      Memory Limit: 65536 KB

Due to the successful resist in Under Attack II, the enemy lost most of their bombers and our ground forces are advancing for victory. However, our spy has transmitted a shocking intel saying that the insane and desparate enemy set up a crazy plan aiming at our civilians. They will launch nuclear missles to attack prosperous cities in our country ! Doctor has received order from central command to calculate how many cities will be destroyed if the enemy bomber succeed (though the possibility is very little).

According to intel, every nuclear missle has a effect range. The missle's effect range is a ellipse with axis length a parrelling to x axis, axis length b parrelling to y axis.Notice enemy can attack every point. Our spies have got data of the ellipse of missle and now given the cooridinate of cities, please show how many cities will be attacked at most.

Input

The input consists of multiple cases.
The first line are the length a and b of effect ellipse's axises. a b are both in the range of [0,400].a b are both positive floating numbers.
Next line is city number n.n can be up to 200.
Following n lines are x and y non-negative floating numbers cooridinate of each city.
Cities on the edge of ellipse are also regarded as attacked. It's guaranteed that no two cities are at one point.

Output

Output the cities affected at most.

Sample Input

2 3
2
1 1
2 2

Sample Output

2

Author: HE, Qidan
Contest: ZOJ Monthly, February 2012
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